For image projection on a general planar projection screen, the image projected will suffer distortion unless the projector is placed in a predesigned position relative to that of the projection screen. Standard types of projectors have a function that corrects the distortion. The projectors use this distortion-correcting function to counteract the distortion by deforming the unprojected image inversely to the distortion (image deformation) caused by the projection from a non-assumed position or direction, and then projecting the image whose distortion has been corrected by the deformation. To implement this function, it is necessary to acquire beforehand the mappings that represent a shape of the projection screen and the deformation level of the image that is dictated by a posture and a positional relationship between the projection screen and the projector. The deformation level here refers to how far from current positions the pixels in the image projected will deviate when the image is actually projected.
Various methods are proposed for acquiring the mappings. The techniques utilizing the fact that the mappings become the projective transformation determinable with a minimum number of parameters are proposed for a planar projection screen, in particular. Examples of these techniques are by manually entering positions at four corners of the image, or by projecting a test pattern and then after automatically detecting a marker, edges of the image, edges of the screen, or the like, from a camera-acquired image of the projected test pattern, calculating the parameters relating to the projective transformation. Patent Document 1 describes a method used to project an image by acquiring one piece of information on a distance between the projector and the screen, then estimating, from the acquired distance information and a shape of the screen, mutual distances between four corner positions on the screen, and after correcting the shape of the screen, deforming the image to be projected, according to the corrected screen shape.
Patent Document 2 describes an image projection system that obtains high-resolution projection images by detecting feature points very accurately with a laser pointer or the like, or by sequentially updating parameter settings relating to tilting, rotation, and shifting.
Patent Document 3 describes a plane projection apparatus that uses a projection region and a planar projective transformation matrix to transform images geometrically. The transformation is conducted by: creating and projecting a predetermined pattern image, then determining, from a photographic image obtained by first photographing the projected image, points on the projected image that correspond to points on the photographic image, next after listing the thus-determined corresponding points, clustering the points of the photographic image on an in-space plane-by-plane basis using the planar projective transformation matrix derived from the listed corresponding points, and determining the projection region from the plane-by-plane clustered points on the photographic image.
Patent Document 4 describes a method of calculating parameters relating to a quadratic surface assumed beforehand as a shape of a projection screen. Patent Document 4 also describes a method of composite image generation, in which method, images from a plurality of projectors are represented in undistorted form on a quadratic surface screen. In the methods of Patent Document 4, a mapping function that represents correspondence between a first onscreen-projected point as viewed from a coordinate system of each projector, and the first onscreen-projected point as viewed from any assumed viewing point, and an inverse function are calculated and distortion is corrected using the inverse function that relates to mapping in each projector. During the calculation of the mapping function and the inverse function, a matrix M for conversion from a fundamental coordinate system into a viewing point coordinate system, and a matrix S for converting camera coordinates into the fundamental coordinate system are first used so that a matrix H for conversion from the viewing point coordinate system into the camera coordinate system will be obtained for predetermined test-pattern points projected on the quadratic surface screen from the projectors. The conversion matrix H is next used to calculate a quadratic surface parameter Qv in the viewing point coordinate system with the assumed viewing point as its origin, from a quadratic surface parameter Q derived in the camera coordinate system. The quadratic surface parameter Qv is used after that to calculate a mapping function that represents correspondence between a second onscreen-projected point as viewed from an i-coordinate system of the projector, and the second onscreen-projected point as viewed from another assumed viewing point, and then to calculate an inverse function from the mapping function.